# Functionel Programming - Assignments
###### tags: `F#`

## Assignment 01

module Programfs

open System

// exericse 1.1
let sqr x = x * x;;   

// exercise 1.2
let pow x n = System.Math.Pow(x,n);;
// ikke komma...

// exercise 1.3
let rec sum = function 
    |0 -> 1
    |n -> n + sum(n-1);;

// exercise 1.4 
let rec fib = function
    |0 -> 0
    |1 -> 1
    |n -> fib(n-1) + fib(n-2);;
// if-then-else 

// exercise 1.5
let rec fact=
    function
    |0 -> 1
    |n -> n * fact(n-1)

let rec power =
    function 
    |(x,0) -> 1.0
    |(x,n) -> x * power(x, n-1)    

//1.5A
// Type: float * int

// 1.5B
// Type: int

// 1.5C
// Type: float 

// 1.5D
// Type: (float * int -> float) * (int -> int)
 
// Exercise 1.6 
let dup (s:string) = s + s

// Exercise 1.7
let rec dupn (s : string) = function
    |0 -> ""
    |x -> s ^ dupn s (x-1)

// Exercise 1.8
let rec bin = function
    |(n,0) ->  1
    |(n,k) when k=n -> 1 
    |(n,k) -> bin (n-1, k-1) + bin(n-1, k)
// match statement...

// Exercise 1.9
let rec f =
    function
    |(0,y) -> y
    |(x,y) -> f(x-1, x*y)

// 1) type of f: int * int -> int

// 2) when x = 0

// 3) 
// a) 
(* *
f(2,3): The arguement matches the pattern (n, k) in the first clause 
giving the binding n |-> 2 and k |-> 3
bindings: 
f(x,y) ~> (f(m,n), [m |-> x, n |-> y])

f(2,3)
~> f(x-1, x*y), [m |-> 2, n |-> 3]
~> f(2-1, 2*3)
~> f(1, 6)
* *)

//4
// if a_1 and a_2 are values of type T1 and T2 then (a_1,a_2) is a value of type T1*T2

// Exercise 1.10
let test(c,e) = if c then e else 0

// a) bool * int -> int 

// b) 
(*
    test(false, fact(-1))
    ~> test(0) ---> 0
*)

// c)
// infinte evaluation because applying fact to a negative 
//integer leads to an inifinite evaluation. 

// Exercise 1.11

// curry:
let curry f = fun a -> fun b -> f (a,b);;

// uncurry:
let uncurry g = fun (a,b)  -> g a b

// Exercise 1.12
let empty (letter: char, pointValue: int) = fun (pos: int) -> (letter, pointValue)

// Exercise 1.13
let add newPos (letter: char, pointValue: int) word pos =
    if newPos = pos then (letter, pointValue)
    else word pos

// Exercise 1.14
let hello = empty('H',4) |> add 1 ('E',1) |> add 2 ('L',1) |> add 3 ('L',1) |> add 4 ('O',1)

// Exercise 1.15
let singleLetterScore word pos = match word(pos) with
    |(_,pointValue) -> pointValue 

let doubleLetterScore word pos = match word(pos) with
    |(_,pointValue) -> pointValue * 2

let trippleLetterScore word pos = match word(pos) with
    |(_,pointValue) -> pointValue 

## Assignment 02